






'''simple docstring'''







class   __SCREAMING_SNAKE_CASE       :


  """simple docstring"""


  def __init__(			self   ,	UpperCamelCase__   ,	UpperCamelCase__   ,	UpperCamelCase__	):






         """simple docstring"""


         a_						     =			None
         a_						     =			None
         a_						     =			graph

         self._normalize_graph(UpperCamelCase__   ,	UpperCamelCase__	)
         a_						     =			len(UpperCamelCase__	)
         a_						     =			None







  def    _a       (			self   ,	UpperCamelCase__   ,	UpperCamelCase__	):






         """simple docstring"""


         if sources is int:
                a_						     =			[sources]
         if sinks is int:
                a_						     =			[sinks]

         if len(UpperCamelCase__	) == 0 or len(UpperCamelCase__	) == 0:
                return

         a_						     =			sources[0]
         a_						     =			sinks[0]

         # make fake vertex if there are more
         # than one source or sink
         if len(UpperCamelCase__	) > 1 or len(UpperCamelCase__	) > 1:
                a_						     =			0
                for i in sources:
                       max_input_flow += sum(self.graph[i]	)

                a_						     =			len(self.graph	) + 1
                for room in self.graph:
                       room.insert(0   ,	0	)
                self.graph.insert(0   ,	[0] * size	)
                for i in sources:
                       a_						     =			max_input_flow
                a_						     =			0

                a_						     =			len(self.graph	) + 1
                for room in self.graph:
                       room.append(0	)
                self.graph.append([0] * size	)
                for i in sinks:
                       a_						     =			max_input_flow
                a_						     =			size - 1







  def    _a       (			self	):






         """simple docstring"""


         if self.maximum_flow_algorithm is None:
                raise Exception('You need to set maximum flow algorithm before.'	)
         if self.source_index is None or self.sink_index is None:
                return 0

         self.maximum_flow_algorithm.execute()
         return self.maximum_flow_algorithm.getMaximumFlow()







  def    _a       (			self   ,	UpperCamelCase__	):






         """simple docstring"""


         a_						     =			algorithm(self	)





class   __SCREAMING_SNAKE_CASE       :


  """simple docstring"""


  def __init__(			self   ,	UpperCamelCase__	):






         """simple docstring"""


         a_						     =			flow_network
         a_						     =			flow_network.verticesCount
         a_						     =			flow_network.sourceIndex
         a_						     =			flow_network.sinkIndex
         # it's just a reference, so you shouldn't change
         # it in your algorithms, use deep copy before doing that
         a_						     =			flow_network.graph
         a_						     =			False







  def    _a       (			self	):






         """simple docstring"""


         if not self.executed:
                self._algorithm()
                a_						     =			True







  def    _a       (			self	):






         """simple docstring"""


         pass





class   __SCREAMING_SNAKE_CASE       (__A       ):


  """simple docstring"""


  def __init__(			self   ,	UpperCamelCase__	):






         """simple docstring"""


         super().__init__(UpperCamelCase__	)
         # use this to save your result
         a_						     =			-1







  def    _a       (			self	):






         """simple docstring"""


         if not self.executed:
                raise Exception('You should execute algorithm before using its result!'	)

         return self.maximum_flow





class   __SCREAMING_SNAKE_CASE       (__A       ):


  """simple docstring"""


  def __init__(			self   ,	UpperCamelCase__	):






         """simple docstring"""


         super().__init__(UpperCamelCase__	)

         a_						     =			[[0] * self.verticies_count for i in range(self.verticies_count	)]

         a_						     =			[0] * self.verticies_count
         a_						     =			[0] * self.verticies_count







  def    _a       (			self	):






         """simple docstring"""


         a_						     =			self.verticies_count

         # push some substance to graph
         for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]	):
                self.preflow[self.source_index][nextvertex_index] += bandwidth
                self.preflow[nextvertex_index][self.source_index] -= bandwidth
                self.excesses[nextvertex_index] += bandwidth

         # Relabel-to-front selection rule
         a_						     =			[
             i
             for i in range(self.verticies_count	)
             if i != self.source_index and i != self.sink_index
         ]

         # move through list
         a_						     =			0
         while i < len(UpperCamelCase__	):
                a_						     =			vertices_list[i]
                a_						     =			self.heights[vertex_index]
                self.process_vertex(UpperCamelCase__	)
                if self.heights[vertex_index] > previous_height:
                       # if it was relabeled, swap elements
                       # and start from 0 index
                       vertices_list.insert(0   ,	vertices_list.pop(UpperCamelCase__	)	)
                       a_						     =			0
                else:
                       i += 1

         a_						     =			sum(self.preflow[self.source_index]	)







  def    _a       (			self   ,	UpperCamelCase__	):






         """simple docstring"""


         while self.excesses[vertex_index] > 0:
                for neighbour_index in range(self.verticies_count	):
                       # if it's neighbour and current vertex is higher
                       if (
                           self.graph[vertex_index][neighbour_index]
                           - self.preflow[vertex_index][neighbour_index]
                           > 0
                           and self.heights[vertex_index] > self.heights[neighbour_index]
                       ):
                              self.push(UpperCamelCase__   ,	UpperCamelCase__	)

                self.relabel(UpperCamelCase__	)







  def    _a       (			self   ,	UpperCamelCase__   ,	UpperCamelCase__	):






         """simple docstring"""


         a_						     =			min(
             self.excesses[from_index]   ,	self.graph[from_index][to_index] - self.preflow[from_index][to_index]   ,	)
         self.preflow[from_index][to_index] += preflow_delta
         self.preflow[to_index][from_index] -= preflow_delta
         self.excesses[from_index] -= preflow_delta
         self.excesses[to_index] += preflow_delta







  def    _a       (			self   ,	UpperCamelCase__	):






         """simple docstring"""


         a_						     =			None
         for to_index in range(self.verticies_count	):
                if (
                    self.graph[vertex_index][to_index]
                    - self.preflow[vertex_index][to_index]
                    > 0
                ) and (min_height is None or self.heights[to_index] < min_height):
                       a_						     =			self.heights[to_index]

         if min_height is not None:
                a_						     =			min_height + 1


if __name__ == "__main__":
  __lowerCAmelCase        =							[0]
  __lowerCAmelCase        =							[3]
  # graph = [
  #     [0, 0, 4, 6, 0, 0],
  #     [0, 0, 5, 2, 0, 0],
  #     [0, 0, 0, 0, 4, 4],
  #     [0, 0, 0, 0, 6, 6],
  #     [0, 0, 0, 0, 0, 0],
  #     [0, 0, 0, 0, 0, 0],
  # ]
  __lowerCAmelCase        =							[[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

  # prepare our network
  __lowerCAmelCase        =							FlowNetwork(graph, entrances, exits)
  # set algorithm
  flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
  # and calculate
  __lowerCAmelCase        =							flow_network.find_maximum_flow()

  print(f"""maximum flow is {maximum_flow}""")












'''simple docstring'''







def       __UpperCamelCase					(      lowercase_       :  int = 1_000_000   ):
       """simple docstring"""




       a_						     =			set(range(3   ,       lowercase_   ,       2   )   )
       primes.add(2   )
       for p in range(3   ,       lowercase_   ,       2   ):
              if p not in primes:
                     continue
              primes.difference_update(set(range(p * p   ,       lowercase_   ,       lowercase_   )   )   )

       a_						     =			[float(lowercase_   ) for n in range(limit + 1   )]

       for p in primes:
              for n in range(lowercase_   ,       limit + 1   ,       lowercase_   ):
                     phi[n] *= 1 - 1 / p

       return int(sum(phi[2:]   )   )


if __name__ == "__main__":
  print(f"""{solution() = }""")




